One dimensional solutions of the $\lambda$-self shrinkers

TL;DR

This paper investigates one-dimensional $\lambda$-self shrinkers and demonstrates the existence of additional closed, embedded solutions beyond the circle for specific negative $\lambda$ values.

Contribution

The study identifies new closed, embedded solutions of 1D $\lambda$-self shrinkers for certain negative $\lambda$, expanding understanding of their solution space.

Findings

Existence of closed, embedded solutions other than the circle for some negative $\lambda$

Characterization of solution types depending on $\lambda$

Extension of known solutions in $\lambda$-self shrinker theory

Abstract

In this paper, we study the solution to the 1-dimensional $\lambda$-self shrinkers and show that for certain $\lambda<0$, there are some closed, embedded solutions other than the circle.